olia Oecoomica Stetiesia OI: 10.1515/foli-2016-0038 NOTE TO ATES O ETUN ON OPEN-EN EBT INVESTMENT UNS AN BANK EPOSITS IN POLAN IN THE YEAS 1995 2015 A COMPAATIVE ANALYSIS OLIA OECONOMICA STETINENSIA 16 (1), (2016), 93 112 * Prof. Krzysztof Piasecki Pozań Uiversity of Ecoomics ad Busiess, aculty of Iformatics ad Electroic Ecoomy, epartmet of Operatios esearch Al. Niepodległości 10, 61-875 Pozań, Polad e-mail: krzysztof.piasecki@ue.poza.pl eceived 31 ecember 2016, Accepted 31 ecember 2016 Abstract The mai goal of this paper is a discussio o the correct choice of aualized retur rate. Selected retur rate should be appropriate for the multiaual comparative aalysis of bak deposits ad ivestmet fuds. The whole discussio was based o theoretical cosideratios ad a umerical experimet. Keywords: spot rate, simple aualized retur rate JEL classificatio: G11 * This ote presets the reviewer s polemic with the author. Uautheticated owload ate 1/7/18 1:15 AM
Note to ates of etur o Ope-Ed ebt Ivestmet uds... 251 I will use the fiacial termiology used i (ittma, 2016). I this iterestig paper, bak deposits ad ivestmet fuds are evaluated by their aualized returs rate. A aalysis of the icrease i the value of each of these fiacial assets is carried out for the multiaual holdig period. The process of growth i the value of bak deposit growth is i the process of bak accouts. or the case of a multiaual holdig period, this process should be assessed usig the effective aualized rate of retur. 1 The process of growth i the value of the uit ivestmet fud is the process of capital appreciatio. I the case of the multiaual holdig period, this process should be assessed by meas of the effective aualized rate of retur or by the logarithmical aualized rate of retur. 2 It implies that returs o ivestmet fuds or o bak deposits ca be compared oly by meas effective aualized rate of retur. The comparative aalysis carried out i the paper (ittma, 2016) is based o the followig estimates of retur rates: for bak deposits ( r ) holdig period retur 1 + 1 i 1 i = = = (1) simple aualized et rate of retur 3 o a deposit, r i et (after tax) iterest rate o a oe-year deposit i the i-th year, 4 ivestmet horizo i years; for ivestmets fuds Q S holdig period retur Q simple aualized et rate of retur o a fud, Q S quotatio o the day of the sale of shares by a ivestor, Q B quotatio o the day of the buy of shares by a ivestor, ( 1 P) 1 ( 1 T) B = = (2) 1 efied as spot rate. 2 efied as spot logarithmic rate. 3 efied as omial et iterest rate. 4 i.e. et forward rate i the i-th year. Uautheticated owload ate 1/7/18 1:15 AM
252 Krzysztof Piasecki P distributio fee rate (%), T capital gais tax rate (%), ivestmet horizo i years. ittma (2006) justifies the choice of simple aualized et retur rate as the basis tool for a comparative aalysis i this way that her choice was dictated by the fact that i the case of fuds, there is o capitalizatio of iterest durig the ivestmet period. As is well kow, i the case of fuds, the process of iterest capitalizatio is replaced by the process of capital appreciatio. I additio, ay simple aualized retur rate may be applied oly i the case of a holdig period that is shorter tha oe year. Therefore, above ittma s justificatio is ucovicig. Moreover, ittma (2016) states, that the formula (1) is suggested by Jajuga ad Jajuga (2014). O the other had, we ca see that the holdig period retur is obtaied by meas of compoud aual iterest. I this case, Jajuga ad Jajuga (2014, p. 93) state that ay ivestmet should be evaluated by meas of effective (aualized) rate of retur defied by formula (2.18) i the cited book. Aalogous statemets also are foud, for example i (Jasse et al., 2009) or (Piasecki, oka-chmielowiec, 2011). or this reaso, The comparative aalysis carried out i the paper (ittma, 2016) should be based o the followig estimates of retur rates: for bak deposits: ( ri ) = holdig period retur = 1+ 1 i= 1 effective aualized et rate of retur o a deposit, r i, defied below is formula (1); (1a) for ivestmets fuds Q ( 1 ) 1 ( 1 ) S = holdig period retur = P T QB effective aualized et rate of retur o a fud, Qs, Q B, P, T, defied below is formula (2). (2a) Uautheticated owload ate 1/7/18 1:15 AM
Note to ates of etur o Ope-Ed ebt Ivestmet uds... 253 I have stated thus far that ittma (2016) had applied the wrog theoretical basis for the carried out comparative aalysis. It remais to be clarified whether this error has a sigificat impact o the calculatio carried out. or this purpose let us look at the followig example. Example: We cosider the holdig period from 1995 to 2015. The the ivestmet horizo i years is equal to: = 2015 1995 = 20. Let us assume that et (after tax) iterest rate o a oe-year deposit Piggybak is costat ad it is equal to: r i = 0.05. The we ca calculate: by meas of (1) a simple aualized et rate of retur o a deposit = 0.1653, by meas of (1a) a effective aualized et rate of retur o a deposit = 0.05. It is obvious, that the effective aualized et rate of retur describes Piggybak better tha a simple aualized et rate. We ca see additioally, that the relative error of the calculatio is equal to: δ = 100% = 230%. This example is compellig proof that a formal error which has bee foud ca have a sigificat impact o the comparative aalysis carried out i (ittma, 2016). All of this ca ultimately decide that all of the results preseted i the paper (ittma, 2016) are ureliable. I this situatio, I thik it is ecessary to repeat all of the calculatios i such a way that: formula (1) is replaced by the formula (1a), formula (2) is replaced by the formula (2a). This calculatio the autheticates the obtaied coclusios. I would ot be surprised; as such calculatios udermie the formulated coclusios thus far. Uautheticated owload ate 1/7/18 1:15 AM
254 Krzysztof Piasecki efereces ittma, I. (2016). ates of retur o ope-ed debt ivestmet fuds ad bak deposits i Polad i the years 1995 2015 a comparative aalysis. olia Oecoomica Stetiesia, 16 (1), 93 112. OI: 10.1515/foli-2016-0007. Jasse, J., Maca,., Volpe di Prigao, E. (2009). Mathematical iace. etermiistic ad Stochastic Model. Lodo: Joh Wiley & Sos. Jajuga, K., Jajuga, T. (2014). Iwestycje: istrumety fiasowe, aktywa iefiasowe, ryzyko fiasowe, iżyieria fiasowa. Warszawa: Wydawictwo Naukowe PWN. Piasecki, K., oka-chmielowiec, W. (2011). Matematyka fiasowa. Warszawa: C.H. Beck. Uautheticated owload ate 1/7/18 1:15 AM